Worksheet for solving proportions with step-by-step examples and practice problems.

Let’s solve each proportion step by step using cross products. Remember:
In a proportion like $\frac{a}{b} = \frac{c}{d}$, you multiply diagonally: $a \cdot d = b \cdot c$. Then solve for the variable.

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Problem 1:
$\frac{m}{30} = \frac{28}{40}$

Cross multiply:
$m \cdot 40 = 30 \cdot 28$
$40m = 840$

Divide both sides by 40:
$m = 840 ÷ 40 = 21$

✔ Answer: m = 21

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Problem 2:
$\frac{14}{35} = \frac{18}{p}$

Cross multiply:
$14 \cdot p = 35 \cdot 18$
$14p = 630$

Divide both sides by 14:
$p = 630 ÷ 14 = 45$

✔ Answer: p = 45

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Problem 3:
$\frac{9}{21} = \frac{f}{35}$

Cross multiply:
$9 \cdot 35 = 21 \cdot f$
$315 = 21f$

Divide both sides by 21:
$f = 315 ÷ 21 = 15$

✔ Answer: f = 15

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Problem 4:
$\frac{e}{65} = \frac{8}{13}$

Cross multiply:
$e \cdot 13 = 65 \cdot 8$
$13e = 520$

Divide both sides by 13:
$e = 520 ÷ 13 = 40$

✔ Answer: e = 40

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Problem 5:
$\frac{36}{60} = \frac{x}{45}$

Cross multiply:
$36 \cdot 45 = 60 \cdot x$
$1620 = 60x$

Divide both sides by 60:
$x = 1620 ÷ 60 = 27$

✔ Answer: x = 27

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Problem 6:
$\frac{12}{32} = \frac{36}{n}$

Cross multiply:
$12 \cdot n = 32 \cdot 36$
$12n = 1152$

Divide both sides by 12:
$n = 1152 ÷ 12 = 96$

✔ Answer: n = 96

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Problem 7:
$\frac{43}{o} = \frac{24}{48}$

Cross multiply:
$43 \cdot 48 = o \cdot 24$
$2064 = 24o$

Divide both sides by 24:
$o = 2064 ÷ 24 = 86$

✔ Answer: o = 86

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Problem 8:
$\frac{48}{k} = \frac{16}{35}$

Cross multiply:
$48 \cdot 35 = k \cdot 16$
$1680 = 16k$

Divide both sides by 16:
$k = 1680 ÷ 16 = 105$

✔ Answer: k = 105

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Problem 9:
$\frac{26}{169} = \frac{z}{52}$

Cross multiply:
$26 \cdot 52 = 169 \cdot z$
$1352 = 169z$

Divide both sides by 169:
$z = 1352 ÷ 169 = 8$

✔ Answer: z = 8

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Final Answer:
1. m = 21
2. p = 45
3. f = 15
4. e = 40
5. x = 27
6. n = 96
7. o = 86
8. k = 105
9. z = 8